Scouts are very good for certain things (talent evaluation). Coaches are very good for certain things (tactics, motivation). Those are not the sole priorities of a modern NHL GM -- i.e. what makes a good scout doesn't necessarily translate to general management.
GMs are generally the interface between ownership and operations and the public/media. Depending on the team's management structure and where the chains of command are spooled, it's far more than just making draft picks and chumming up with the buddies and shooting trade ideas.
Where teams have faltered is when they really dig in on one great thing, but the rest of their operation lies fallow. Florida's non-Tallon GMs had pretty excellent talent evaluation, but burned all their relationship bridges (and thus, public perception and support). Buffalo was so focused on tanking that they got pretty solidly stuck. Vancouver's GM has no spine to stand up to ownership and as a result has no draft picks to even leverage his scouting talent.
What Lou, who previously had zero hockey experience when he started, was good at was treating people very well internally (they buy in; there is a ridiculous amount of love and respect for Lou regardless of his hockey decisions out there in the industry), setting up an environment conducive to going about business (leak-free!), and being ice cold in executing business decisions (Robidas Island).
Generally, I think it's a good idea for tear downs to be executed by a different person than the one who first built it, and in turn should be built up again by another person. Lou tore things down excellently: Winnik x2, Polak+Spaling = 2 2nds!, Phanuef, Lupul, Robidas, Olli Jokinen got an asset!. Lou hasn't really built very well in the time he has started pulling things together.
My current theory about the 3-year Lamoriello era is not so much one of apprenticeship as I first surmised, but more like giving time for the true management team to learn to work together. I think Babcock coming in was a bit of a surprise (Guy Boucher was practically touring MLSE offices when the decision came down). I think Shanahan knew the benefits of Babcock on the ice and in the dressing room, but also understanding that the gravity that Babcock exerts on everyone (i.e. the team Shanahan had already built) presented a danger to any new executives working with him.
In comes Lamoriello, who Babcock knows and respects implicitly, and everyone falls in line under that umbrella, while at the same time still falling under Shanahan's umbrella of collaboration. This forces Babcock to work with Dubas and to work with Hunter, to argue their various sides and execute their authority over their domains, with the buck stopping at Lou (who I'm guessing sided with Babcock more often than not).
After 3 years, Babcock has seen what some of Hunter's and Dubas' decisions have wrought: Marner > Hanifin/Werenski/Provorov, the rise of speedy skilled players even on the lower lines, successful Marlies runs. I can imagine Babcock buying in more readily now to whatever Dubas and co. are building.